Abstract
Simulated annealing calculations were performed on a Penrose lattice with the aim of clarifying the relation between the interaction connections and the magnetic orders in the phason space. Alternating signs were assumed in the magnetic interactions up to the second shortest distances between spins. Two different types of long-range antiferromagnetic orders were found for two cases with reversed sign of the interactions. The two types of order were most adequately interpreted as the orders of subdivisions in the occupation domain in the phason space. Reasonable interpretations of the mechanism of the subdivisions are given on the basis of the physical interactions projected to the phason space.
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